It just happens...
Sometimes the puzzle comes up, and your brain kicks in and your fingers just go along without thinking about it. It's fun when that happens. I bet my mom never foresaw the benefits for cryptogram solving that would come of her insisting that I take typing in high school.
Of course, it doesn't always work. I've had some puzzles take me a long time to solve, only to hit the check button and find out that at some point I solved it in record time. It's a bit alarming when I don't even remember ever seeing the quote before.
As for the solving rates, my theory is that there are a lot more people playing than just those on the high scores board, and there are likely many who just skip on to the next one when the pattern doesn't come to them immediately.